Development of an Epidemiological Model with Transmission Matrix to Understand the Dynamics of Tuberculosis Spread

Mathematics Department, Faculty of Mathematic and Sciences, Universitas Tanjungpura, 78124 Indonesia

^* Corresponding author: melianapasaribu@math.untan.ac.id

Abstract

Tuberculosis remains a major challenge in the field of healthcare. The spread of tuberculosis depends on complex interactions between individuals within a population, involving factors such as mobility, physical contact, and age groups. Each age group has unique characteristics that influence how tuberculosis spreads among the population and how each group responds to the infection. To understand the dynamics of tuberculosis spread, an epidemiological model is required. This study aims to develop an epidemiological model based on a transmission matrix that can represent the pattern of tuberculosis spread within a population. The transmission matrix is used to describe the interactions between individuals and subpopulations, taking into account the transmission rate and incubation period. After building the model and transmission matrix, model calibration and validation are conducted. In this stage, model parameters are adjusted to ensure that the model can accurately replicate the observed epidemiological data. Subsequently, analysis is performed using the model and transmission matrix to understand the dynamics of disease spread, followed by interpretation of the results. The findings of this study indicate that the use of the transmission matrix provides valuable insights into the dynamics of tuberculosis spread and helps identify high-risk subpopulations.